In recent years, in radio communications systems, achieving a higher frequency utilization efficiency has become a significant problem. One means of solving this problem is by using error correcting code, which has excellent correction capabilities, and multilevel modulation. For example, in an existing cellular system such as the cdma 2000 HRPD (High Rate Packet Data) system disclosed in Non-patent document 1, an improvement in frequency utilization efficiency is achieved by turbo coding the information bits and using multilevel modulation such as 16 QAM (Quadrature Amplitude Modulation).
Moreover, in Non-patent document 2, low-density parity check codes are disclosed as codes that have even greater correction capabilities than turbo coding. Low-density parity check codes are divided into regular codes in which the weighting distribution of the check matrix is uniform, and irregular codes in which the weighting distribution varies. It is generally considered that irregular codes have greater correction capabilities. For example, in Non-patent document 3, irregular low-density parity check codes that are suitable for puncturing are disclosed. The irregular low-density parity check codes in Non-patent document 3 are binary low-density parity check codes designed as a finite field having an order of 2, and are characterized by the fact that any of the information bit column weightings are larger than a parity bit column weighting. Moreover, in Non-patent document 4, a construction method for binary low-density parity check codes suitable for 16QAM is disclosed as a code construction method suitable for multilevel modulation transmission technology. Moreover, in Non-patent document 5, multilevel modulation technology is disclosed as a coding modulation system which is a combination of error correcting code and multilevel modulation, and which is representative of a coding modulation system in low-density parity check codes, and which employs binary low-density parity check codes that are designed such that the order is a finite field larger than 2.
Moreover, in Non-patent document 6, demodulation technology which is based on turbo coding known as ‘twin turbo decoding’ has been proposed as a demodulation method for improving the correction capability of turbo code. FIG. 29 is a block diagram showing the structure of a twin turbo decoder 201. Here, in a known turbo coder, an information bit vector is taken as Xa, a parity bit vector created by an element coder 1 is taken as Xb, and a parity bit vector created by an element coder 2 is taken as Xc. In a typical turbo decoder, efficient MAP (Maximum A-Posteriori Probability) decoding is achieved by providing a stochastic propagation feedback loop in which two element decoders are interlinked by a bit interleaver, and a-posteriori values of the bits that have been updated in each element decoder are fed back as a-priori values of the other element decoder. In contrast, in the twin turbo decoder 201, by providing a stochastic coupling feedback loop (i.e., in FIG. 29 the path by which a-posteriori values (Xa, Xc) after being output from the element decoder 2_211 are input via the turbo deinterleaver 213 into a demodulator 1_210, and the path by which a-posteriori values (Xa, Xb) after being output from the element decoder 1_211 are input into a demodulator 2_210) in addition to the stochastic propagation feedback loop thereof (i.e., the path in FIG. 29 by which an exterior value (Xa) after being output from an element decoder 2_211 is input as an a-priori value (Xa) into an element decoder 1_211 via a turbo deinterleaver 213), the likelihood coupling probability of each bit making up the multilevel modulation symbol is calculated, thereby improving the error correction capability of the turbo code.
For example, in 4ASK (Amplitude Shift Keying) modulation, if a relationship is obtained for a distance between a transmission signal point and a reception signal point shown in FIG. 30, then the communication path value update processing in the demodulators 1_210 and 2_210 shown in FIG. 29 can be expressed by Formulas (1) and (2).
                    [                  Formula          ⁢                                          ⁢          1                ]                                                                                                                                  L                  c                                ⁡                                  (                                      b                    ⁡                                          (                      0                      )                                                        )                                            =                            ⁢                              min                ⁢                                  {                                                                                    γδ                        C                                            -                                                                        (                                                                                                                    -                                2                                                            ⁢                                                              b                                ⁡                                                                  (                                  1                                  )                                                                                                                      +                            1                                                    )                                                ⁢                                                                                                            L                              p                                                        ⁡                                                          (                                                              b                                ⁡                                                                  (                                  1                                  )                                                                                            )                                                                                /                          2                                                                                      ,                                                                  γδ                        D                                            -                                                                                                                                                                              ⁢                                                      (                                                                                            -                          2                                                ⁢                                                  b                          ⁡                                                      (                            1                            )                                                                                              +                      1                                        )                                    ⁢                                                                                    L                        p                                            ⁡                                              (                                                  b                          ⁡                                                      (                            1                            )                                                                          )                                                              /                    2                                                  }                            -                                                                                        ⁢                              min                ⁢                                  {                                                                                    γδ                        B                                            -                                                                        (                                                                                                                    -                                2                                                            ⁢                                                              b                                ⁡                                                                  (                                  1                                  )                                                                                                                      +                            1                                                    )                                                ⁢                                                                                                            L                              P                                                        ⁡                                                          (                                                              b                                ⁡                                                                  (                                  1                                  )                                                                                            )                                                                                /                          2                                                                                      ,                                                                  γδ                        A                                            -                                                                                                                                                            ⁢                                                (                                                                                    -                        2                                            ⁢                                              b                        ⁡                                                  (                          1                          )                                                                                      +                    1                                    )                                ⁢                                                                            L                      p                                        ⁡                                          (                                              b                        ⁡                                                  (                          1                          )                                                                    )                                                        /                  2                                            }                                                                          =                            ⁢                                                min                  ⁢                                      {                                                                                            γ                          ⁢                                                                                                          ⁢                                                      δ                            C                                                                          +                                                                                                            L                              p                                                        ⁡                                                          (                                                              b                                ⁡                                                                  (                                  1                                  )                                                                                            )                                                                                /                          2                                                                    ,                                                                        γδ                          D                                                -                                                                                                            L                              P                                                        ⁡                                                          (                                                              b                                ⁡                                                                  (                                  1                                  )                                                                                            )                                                                                /                          2                                                                                      }                                                  -                                                                                                      ⁢                              min                ⁢                                  {                                                                                    γδ                        B                                            +                                                                                                    L                            p                                                    ⁡                                                      (                                                          b                              ⁡                                                              (                                1                                )                                                                                      )                                                                          /                        2                                                              ,                                                                  γδ                        A                                            -                                                                                                    L                            P                                                    ⁡                                                      (                                                          b                              ⁡                                                              (                                1                                )                                                                                      )                                                                          /                        2                                                                              }                                                                                        (        1        )                                [                  Formula          ⁢                                          ⁢          2                ]                                                                                                                                  L                  c                                ⁡                                  (                                      b                    ⁡                                          (                      1                      )                                                        )                                            =                            ⁢                              min                ⁢                                  {                                                                                    γδ                        C                                            -                                                                        (                                                                                                                    -                                2                                                            ⁢                                                              b                                ⁡                                                                  (                                  0                                  )                                                                                                                      +                            1                                                    )                                                ⁢                                                                                                            L                              p                                                        ⁡                                                          (                                                              b                                ⁡                                                                  (                                  0                                  )                                                                                            )                                                                                /                          2                                                                                      ,                                                                  γδ                        B                                            -                                                                                                                                                                              ⁢                                                      (                                                                                            -                          2                                                ⁢                                                  b                          ⁡                                                      (                            0                            )                                                                                              +                      1                                        )                                    ⁢                                                                                    L                        p                                            ⁡                                              (                                                  b                          ⁡                                                      (                            0                            )                                                                          )                                                              /                    2                                                  }                            -                              min                ⁢                                  {                                                            γδ                      D                                        -                                                                                                                                        ⁢                                                                    (                                                                                            -                          2                                                ⁢                                                  b                          ⁡                                                      (                            0                            )                                                                                              +                      1                                        )                                    ⁢                                                                                    L                        p                                            ⁡                                              (                                                  b                          ⁡                                                      (                            0                            )                                                                          )                                                              /                    2                                                  ,                                                      γδ                    A                                    -                                                                                                                      ⁢                                                (                                                                                    -                        2                                            ⁢                                              b                        ⁡                                                  (                          0                          )                                                                                      +                    1                                    )                                ⁢                                                                            L                      p                                        ⁡                                          (                                              b                        ⁡                                                  (                          0                          )                                                                    )                                                        /                  2                                            }                                                                          =                            ⁢                                                min                  ⁢                                      {                                                                                            γδ                          C                                                +                                                                                                            L                              p                                                        ⁡                                                          (                                                              b                                ⁡                                                                  (                                  0                                  )                                                                                            )                                                                                /                          2                                                                    ,                                                                        γδ                          B                                                -                                                                                                            L                              p                                                        ⁡                                                          (                                                              b                                ⁡                                                                  (                                  0                                  )                                                                                            )                                                                                /                          2                                                                                      }                                                  -                                                                                                      ⁢                              min                ⁢                                  {                                                                                    γδ                        D                                            +                                                                                                    L                            p                                                    ⁡                                                      (                                                          b                              ⁡                                                              (                                0                                )                                                                                      )                                                                          /                        2                                                              ,                                                                  γδ                        A                                            -                                                                                                    L                            p                                                    ⁡                                                      (                                                          b                              ⁡                                                              (                                0                                )                                                                                      )                                                                          /                        2                                                                              }                                                                                        (        2        )            
Wherein Lc(b(0)) and Lc(b(1)) represent communication path values of bits b (0) and b (1), Lp(b(0)) and Lp(b(1)) represent a-priori values of bits b (0) and b (1), and γ represents a signal-to-noise power ratio.
The communication path value of the bit b (0) is updated by the a-posteriori value of its pair bit (b) 1. The communication path value of the other bit b (1) is updated by the a-posteriori value of its pair bit (b) 0.
Moreover, according to Non-patent document 7, it has been reported that in multilevel modulation the error rate varies depending on bit position of the modulation symbols.
Moreover, in new-generation mobile communication systems, it has been observed that multi-carrier transmission systems are becoming prevalent over single carrier transmission systems. Representative multi-carrier transmission systems include OFDM (Orthogonal Frequency Division Multiplexing) systems and MC-CDMA (Multi-carrier-Code Division Multiple Access) systems. According to an MC-DCMA system, by spreading modulation symbols over a plurality of sub-carriers, multiplexing them, and then transmitting them, a frequency diversity effect is obtained. In addition to this, inter-cell interference can be uniformized. However, it is known that, because inter-code interference is generated in the frequency selective transmission path, there is a deterioration in the signal-to-noise and signal-to-interference-energy ratios after back-diffusion (for example, see Non-patent document 8). Therefore, investigations are being made into demodulation methods that estimate a maximum likelihood without any back-diffusion. Using as an example a forward link that performs time division multiplexing on a pilot signal and a data signal and then transmits these, a description is given below of an MC-CDMA system that estimates a maximum likelihood without performing back-diffusion.
FIG. 31 is a block diagram showing the structure of an MC-CDMA data transmission system that estimates a maximum likelihood without performing back-diffusion. Here, in order to simplify the explanation, it is assumed that all the information bits are transmitted using a single MC-CDMA symbol. Firstly, in a transmitter 1000a, a modulator 1040 modulates information bits so as to obtain an nm-th modulation symbol Mt (nm). Next, for the diffusion, the modulation symbol Mt (Nm) is allocated to an id-th frequency band that has a bandwidth equivalent to the bandwidth occupied by the diffusion code, and is converted into a parallel signal by a serial/parallel converter 1050. Next, the modulation symbol that has been allocated to the id-th frequency band is diffused by a different diffusion symbol for each modulation symbol by a diffuser 1060, and is multiplexed to become a data sub-carrier. The modulation symbols have the relationship shown in Formula (3).
                    [                  Formula          ⁢                                          ⁢          3                ]                                                                                                                                                      M                    ^                                    t                                ⁡                                  (                                                            i                      d                                        ,                                                                  n                        ^                                            m                                                        )                                            =                            ⁢                                                                    M                    ^                                    t                                ⁡                                  (                                                                                    (                                                                              n                            m                                                    -                                                                                    n                              m                                                        ⁢                            mod                            ⁢                                                                                                                  ⁢                                                          M                              w                                                                                                      )                                            /                                              M                        w                                                              ,                                                                  n                        m                                            ⁢                      mod                      ⁢                                                                                          ⁢                                              M                        w                                                                              )                                                                                                        =                            ⁢                                                                    M                    t                                    ⁡                                      (                                          n                      m                                        )                                                  ⁢                                  {                                                                                                              0                          ≤                                                      n                            m                                                    ≤                                                                                                                    (                                                                                                      M                                    w                                                                    /                                                                      N                                    w                                                                                                  )                                                            ⁢                                                              N                                d                                                                                      -                            1                                                                                                                                                                                        0                          ≤                                                                                    n                              ^                                                        m                                                    ≤                                                                                    M                              w                                                        -                            1                                                                                                                                                                                        0                          ≤                                                      i                            d                                                    ≤                                                                                                                    N                                d                                                            /                                                              N                                w                                                                                      -                            1                                                                                                                                                                                                      (        3        )            
wherein {circumflex over (M)}t(id,{circumflex over (n)}m) is the {circumflex over (n)}m-th modulation symbol that has been allocated to the idth frequency band, Nw is the diffusivity, Mw is the number of code-multiplexing, and Nd is the data sub-carrier number.
As a result, Formula (4) is obtained.
                    [                  Formula          ⁢                                          ⁢          4                ]                                                                                                D              ^                        t                    ⁡                      (                                          i                d                            ,                                                k                  ^                                d                                      )                          =                              1                                          M                w                                              ⁢                                    ∑                                                n                  ^                                =                0                                                              M                  w                                -                1                                      ⁢                                                                                M                    ^                                    t                                ⁡                                  (                                                            i                      d                                        ,                                                                  n                        ^                                            m                                                        )                                            ⁢                                                c                  w                                ⁡                                  (                                                                                    n                        ^                                            m                                        ,                                                                  k                        ^                                            d                                                        )                                                                                        (        4        )            
wherein {circumflex over (D)}t(id,{circumflex over (k)}d) is the {circumflex over (k)}d-th sub-carrier of the id-th frequency band, and cw({circumflex over (n)}m,{circumflex over (k)}d) is the diffusion code of the {circumflex over (n)}m-th modulation symbol. In addition, 0≦{circumflex over (k)}d≦Nw−1.
Generally, in an MC-CDMA system, orthogonal code such as Walsh's code or the like is used as the diffusion code, and the orthogonal code has characteristics such as those shown in Formulas (5) and (6) below.
                    [                  Formula          ⁢                                          ⁢          5                ]                                                                                  c            w                    ⁡                      (                          m              ,              k                        )                          =                              1            ⁢                                                  ⁢            or                    ⁢                                          -          1                                    (        5        )                                [                  Formula          ⁢                                          ⁢          6                ]                                                                                  ∑                                          k                d                            =              0                                                      N                w                            -              1                                ⁢                                                    c                w                            ⁡                              (                                  m                  ,                  k                                )                                      ⁢                                          c                w                            ⁡                              (                                  n                  ,                  k                                )                                                    =                  {                                                                      N                  w                                                                                                  for                    ⁢                                                                                  ⁢                    m                                    =                  n                                                                                    0                                                                                  for                    ⁢                                                                                  ⁢                    m                                    ≠                  n                                                                                        (        6        )            
As a result, the correlation values between the same codes form the serial length thereof, and the correlation values between different codes becomes [0].
Next, the data sub-carrier is converted into a signal of a time domain by inverse Fourier transform performed by an inverse Fourier transformer 1070, and is then converted into a serial signal by a parallel/serial converter 1080. A cyclic prefix is then inserted by a cyclic prefix inserter 1090, and it is then further time multiplexed with a pilot signal by a time multiplexer 1100, and is transmitted from the transmitter 1000a. 
After signals transmitted from the transmitter 1000a have been affected by the frequency selectivity of a frequency selective transmission path 3010, and have also been affected by noise from an additive white Gaussian noise transmission path 3020, they are received by a receiver 2000a. In the receiver 2000a, the received signal is separated into the pilot signal and data signal by a time division demultiplexer 2010, and the cyclic prefixes are removed therefrom respectively by cyclic prefix removers 2020 and 2090. Next, the signals are converted into parallel signals by serial/parallel converters 2030 and 2100, and are then converted respectively into a data sub-carrier and a pilot sub-carrier by Fourier transform performed by Fourier transformers 2040 and 2110. Transmission path variations are then estimated from the pilot sub-carrier by a transmission path estimator 2120, and equalization (i.e., phase rotation compensation) of the data sub-carrier is performed by an equalizer 2050. The equalized data sub-carrier is expressed by Formula (7).
                    [                  Formula          ⁢                                          ⁢          7                ]                                                                                                D              ^                        eql                    ⁡                      (                                          i                d                            ,                                                k                  ^                                d                                      )                          =                                                                              H                  ^                                est                *                            ⁡                              (                                                      i                    d                                    ,                                                            k                      ^                                        d                                                  )                                                                                                                        H                    ^                                    est                                ⁡                                  (                                                            i                      d                                        ,                                                                  k                        ^                                            d                                                        )                                                                            ⁢                                                    D                ^                            r                        ⁡                          (                                                i                  d                                ,                                                      k                    ^                                    d                                            )                                                          (        7        )            
wherein {circumflex over (D)}r(id,{circumflex over (k)}d) is the reception data sub-carrier, {circumflex over (D)}eql(id,{circumflex over (k)}d) is the data sub-carrier after equalization, and Ĥest(id,{circumflex over (k)}d) is the transmission path estimation value. In addition, Ĥ(id,{circumflex over (k)}d) is the frequency selectivity from the frequency selective transmission path 3010, N0 is the noise power density from the additive white Gaussian noise transmission path 3020, and * shows a complex conjugate.
Next, the equalized data sub-carrier is converted into a serial signal by a parallel/serial converter 2060, and is then converted into a maximum likelihood estimation symbol by a maximum likelihood estimation symbol creator 2070. For example, when the diffusivity is 2, the symbol for maximum likelihood estimation is shown by Formula (8).
                    [                  Formula          ⁢                                          ⁢          8                ]                                                            {                                                                                                                        M                      ^                                        rml                                    ⁡                                      (                                                                  i                        d                                            ,                                              2                        ⁢                                                  n                          ^                                                                                      )                                                  =                                                      Im                    ⁡                                          [                                                                                                    D                            ^                                                    eql                                                ⁡                                                  (                                                                                    i                              d                                                        ,                                                          2                              ⁢                                                              n                                ^                                                                                                              )                                                                    ]                                                        +                                      j                    ⁢                                                                                  ⁢                                          Im                      ⁡                                              [                                                                                                            D                              ^                                                        eql                                                    ⁡                                                      (                                                                                          i                                d                                                            ,                                                                                                2                                  ⁢                                                                      n                                    ^                                                                                                  +                                1                                                                                      )                                                                          ]                                                                                                                                                                                                                                M                      ^                                        rml                                    ⁡                                      (                                                                  i                        d                                            ,                                                                        2                          ⁢                                                      n                            ^                                                                          +                        1                                                              )                                                  =                                                      Re                    ⁡                                          [                                                                                                    D                            ^                                                    eql                                                ⁡                                                  (                                                                                    i                              d                                                        ,                                                          2                              ⁢                                                              n                                ^                                                                                                              )                                                                    ]                                                        +                                      j                    ⁢                                                                                  ⁢                                          Re                      ⁡                                              [                                                                                                            D                              ^                                                        eql                                                    ⁡                                                      (                                                                                          i                                d                                                            ,                                                                                                2                                  ⁢                                                                      n                                    ^                                                                                                  +                                1                                                                                      )                                                                          ]                                                                                                                                                    (        8        )            
wherein {circumflex over (M)}rml(id,{circumflex over (n)}ml) is the {circumflex over (n)}ml-th symbol for maximum likelihood estimation. In addition, 0≦{circumflex over (n)}ml≦Nw−1 and 0≦{circumflex over (n)}ml≦Nw/2−1.
Next, a demodulator 2080a obtains a reception modulation symbol Mr(nm) using Formula (9).[Formula 9]Mr(nm)={circumflex over (M)}rml({circumflex over (n)}ml+idMw)={circumflex over (M)}r(id,{circumflex over (n)}ml)  (9)
The processing to create the symbol for maximum likelihood estimation when the diffusivity is 2 is shown in FIG. 32.
Moreover, according to Non-patent document 4, it has been reported that in multilevel modulation the error rate differs depending on the bit position of the modulation symbol.    [Non-patent document 1] 3GPP2, C.S0024 Version 4.0, “cdma2000 High Rate Packet Data Air Interface Specification,” October 2002.    [Non-patent document 2] Tadashi Wadayama, “Low Density Parity Check Codes and Decoding Method For These”, Shingaku Giho, MR2001-83, December 2001.    [Non-patent document 3] Jin Jeon and Toshinori Suzuki, “A Proposal of Rate-Compatible Low-Density Parity-Check Code for Land Mobile Radio”, Shingaku Giho, IT20051-5, May. 2005.    [Non-patent document 4] Shigeru Uchida, Wataru Matsumoto, Akira Otsuka, and Keishi Murakami, Shingaku Tsuso, “Examination of LDPC Code Construction Methods Suitable for Multilevel Modulation”, B-5-59, September, 2004.    [Non-patent document 5] M. C. Davey and D. MacKay, “Low-Density Parity Check Codes over GF(q),” IEEE Comun. Lett., Vol. 2, No. 6, pp. 165-167, June 1998.    [Non-patent document 6] T. Suzuki, N. Miyazaki, Y. Hatakawa, “A Proposal of Twin Turbo Detector and Its Evaluation for M-QAM OFDM,” Shingaku Tsuso, B-5-6, September 2005.    [Non-patent document 7] N. Miyazaki, C. Zheng, T. Suzuki, and H. Shinonaga, “A Study on Symbol and Sub-Carrier Mapping Techniques for MC-CDMA based on LDPC Code with Progressively Increased Column-Weight,” Proc. PIMRC 2005, B01-4, September 2005.    [Non-patent document 8] N. Miyazaki and T. Suzuki, “A Study on Forward Link Capacity in MC-CDMA Cellular System with MMSEC Receiver,” IEICE Trans. Commun., Vol. E88-B, No. 2, pp. 585-593, February 2005.